J-03 — reading a cross-section

slice the beam. see what the fibers feel.

cross-section stress viewer

cut the section. read the stress map.

See how stress distributes across a rectangular cross-section under axial, bending, and combined loading.

loading type
applied loads
P (kips) 200
M (k-ft) 100
cross-section
b (in) 8
d (in) 18
—
extreme fiber stress
compression
live equation
—
σ = Force per unit area perpendicular to the cut face
P = Force along the member axis
M = Moment causing the linear stress variation
y = Distance from the neutral axis to the point of interest
explained
The stress formula changes with loading type. Under axial load, σ = P/A is uniform. Under bending, σ = My/I varies linearly with distance from the neutral axis. Combined loading adds both: σ = P/A + My/I. The extreme fiber — farthest from the neutral axis — always has the highest stress.
key concepts
what it shows A stress diagram shows what the material is experiencing at one cross-section

Imagine slicing through a beam at a single point and looking at the exposed face. The stress diagram shows the intensity of internal force (stress) at every fiber across the depth. Under axial load it's uniform. Under bending it varies linearly — maximum at the extremes, zero at the center. Combined loading shifts and skews the distribution.

the neutral axis Under bending, there is always a line of zero stress inside the section

The neutral axis is the depth at which bending stress transitions from compression to tension — stress is zero there. For a symmetric section under pure bending, the neutral axis is at the centroid (mid-depth). When axial load is added, the neutral axis shifts toward the tension side because compression is now biased by the axial stress. If the axial load is large enough, the entire section goes into compression and the neutral axis moves outside the section entirely.